Computation of Gaussian orthant probabilities in high dimension

We study the computation of Gaussian orthant probabilities, i.e. the probability that a Gaussian falls inside a quadrant. The Geweke-Hajivassiliou-Keane (GHK) algorithm [Genz, 1992; Geweke, 1991; Hajivassiliou et al., 1996; Keane, 1993], is currently used for integrals of dimension greater than 10. In this paper we show that for Markovian covariances GHK can be interpreted as the estimator of the normalizing constant of a state space model using sequential importance sampling (SIS). We show for an AR(1) the variance of the GHK, properly normalized, diverges exponentially fast with the dimension. As an improvement we propose using a particle filter (PF). We then generalize this idea to arbitrary covariance matrices using Sequential Monte Carlo (SMC) with properly tailored MCMC moves. We show empirically that this can lead to drastic improvements on currently used algorithms. We also extend the framework to orthants of mixture of Gaussians (Student, Cauchy etc.), and to the simulation of truncated Gaussians

An efficient technique based on polynomial chaos to model the uncertainty in the resonance frequency of textile antennas due to bending

The generalized polynomial chaos theory is combined with a dedicated cavity model for curved textile antennas to statistically quantify variations in the antenna's resonance frequency under randomly varying bending conditions. The nonintrusive stochastic method solves the dispersion relation for the resonance frequencies of a set of radius of curvature realizations corresponding to the Gauss quadrature points belonging to the orthogonal polynomials having the probability density function of the random variable as a weighting function. The formalism is applied to different distributions for the radius of curvature, either using a priori known or on-the-fly constructed sets of orthogonal polynomials. Numerical and experimental validation shows that the new approach is at least as accurate as Monte Carlo simulations while being at least 100 times faster. This makes the method especially suited as a design tool to account for performance variability when textile antennas are deployed on persons with varying body morphology

Coarse Grained Computations for a Micellar System

We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms) and atomistic simulations of the Larson model of micelle formation. The procedure hinges on the (expected) evolution of a few slow, coarse-grained mesoscopic observables of the MC simulation, and on (computational) time scale separation between these and the remaining "slaved", fast variables. Short bursts of appropriately initialized atomistic simulation are used to estimate the (coarse-grained, deterministic) local dynamics of the evolution of the observables. These estimates are then in turn used to accelerate the evolution to computational stationarity through traditional continuum algorithms (forward Euler integration, Newton-Raphson fixed point computation). This "equation-free" framework, bypassing the derivation of explicit, closed equations for the observables (e.g. equations of state) may provide a computational bridge between direct atomistic / stochastic simulation and the analysis of its macroscopic, system-level consequences